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Cylinder

Master cylinder with interactive lessons and practice problems! Designed for students like you!

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Cylinder

Study Guide

Key Definition

A cylinder is a 3D shape with two parallel circular bases connected by a curved surface. The bases are congruent and parallel.

Important Notes

A right cylinder means the axis is perpendicular to the bases.
The radius of the cylinder is the radius of its base.
The height is the perpendicular distance between the bases.
The volume formula is $V = \pi r^2 h$.
The surface area formula is $A = 2\pi rh + 2\pi r^2$.

Mathematical Notation

$r$ = radius of the base

$h$ = height of the cylinder

$V$ = volume

$A_L$ = lateral surface area

Remember to use proper notation when solving problems

Why It Works

The formulas for volume and surface area derive from the properties of circles and rectangles forming the bases and side.

Remember

Always distinguish between right and oblique cylinders as it affects surface area calculations but not volume.

Quick Reference

Volume:$V = \pi r^2 h$

Surface Area:$A = 2\pi rh + 2\pi r^2$

Understanding Cylinder

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Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

A cylinder has two congruent circular bases and a curved surface joining them. The height is the distance between the bases.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the volume of a cylinder with radius $r = 3$ and height $h = 5$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

A cylindrical water tank with radius $r = 4$ meters and height $h = 10$ meters needs to be painted. Only the curved surface (lateral area) is to be painted; the circular ends are not painted. Calculate the area that needs painting.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Determine the difference in volume between a right cylinder and an oblique cylinder with the same base radius and height.

Challenge Quiz

Single Choice Quiz

Advanced

Calculate the lateral surface area of a cylinder with radius $r = 5$ and height $h = 12$.

Recap

Watch & Learn

Review key concepts and takeaways